Alena Scott

Rice-Houston AGEP
Rice University, Houston, TX

Wavelet methodology has demonstrated great success in many arenas, but Alena focuses on problems of estimating signals contaminated by noise. A common feature of these problems is the replacement of the raw wavelet coefficients by “smoother” estimates. Typically, some wavelet coefficients are set to zero, i.e. thresholded, while many others are shrunk towards zero. While many wavelet shrinkage techniques assume independence of the wavelet coefficients, empirical evidence suggests that the coefficients are in fact not independent. Therefore, Alena believes that a good thresholding algorithm should take this dependence into account. In addition to capturing the correlation between the coefficients, the threshold level should also depend upon the complexity of the signal being modeled and the level of noise in the sampled signal. Her research is to find an adaptive threshold using a new technique in density estimation, L2E. By adaptive, she means: 1) the algorithm should be automatic and data based and 2) the algorithm should find the best threshold given a particular w, the percentage of the signal that is noise. An estimate for w can be found through partial density estimation with L2E. Using L2E to construct multivariate density estimates for the noise components, she will also attempt to capture the information on intra-scale dependencies. (Rice University, 2005)